We need a formal standard definition of a topological sandwich. First attempt: A topological sandwich is a topological space S = B ∪ M ∪ B', such that: 1) Each of B, M, B' is homeomorphic to the unit ball, 2) Every path from a point of B to a point of B' intersects M.
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If one uses my minimal definition of sandwich, then I conjecture that generalized sandwiches (spaces constructed by surgery on minimal sandwiches) are equivalent presandwiches (spaces meeting the locally sandwich criterion).
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equivalent *to* presandwiches (which I think is a less awkward term than 'protosandwiches')
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If I understand this correctly, presandwiches are decomposable into disjoint sets, one which is minimally sandwich in every nhood and one which is only presandwich in every nhood?
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A space P = B ∪ M ∪ B' is locally sandwich if: Every point p in P has an open neighborhood S_p, such that: S_p = (S_p ∩ B) ∪ (S_p ∩ M) ∪ (S_p ∩ B') is a (minimal) sandwich.
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Right! I was confusing this with our protosandwich discussion we had earlier.
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.